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Astron. Astrophys. 348, 1035-1039 (1999)

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2. Method used by the program to detect new TNOs

The main criteria used by the program to detect new TNOs are the same as those described by Jewitt & Luu (1988) and used with a manual blinking method: (a) the detected objects must exhibit linear and constant velocity motion among the different images, (b) the image shape of the object must be consistent with a point-like object (i.e. with the seeing), (c) the brightness of the object must be constant among images and (d) the rate of motion must be in agreement with a TNO (i.e. less than about 4 arcsec/hr).

In order to limit the number of false detections, we have added to these criteria apparent motion constraints with respect to the ecliptic plane, chosen by the user. The user specifies two limit angles to compare with a vector direction, the purpose being to eliminate "impossible" motions. A test is also performed with the seeing value in order to check if the lack of detection in a single image can be attributed to poor seeing conditions.

As the purpose of the program is to be as automatic as possible, the following steps are used to detect the TNOs from a set of at least three images of a same field of view:

(i) An analysis of each image is performed in using the tools available from MIDAS in order to detect all the objects appearing in each image and to estimate their size and brightness. The key parameter to this analysis is the threshold of detection, which is available as a free parameter for the user. The results are stored in special files.

(ii) From the list of objects obtained with step (i), some of them that can be considered as false detections (i.e. mainly cosmic rays or bad pixels) are eliminated from the files in order to reduce the number of false TNO detections. The criterion used to eliminate these detections is their size: all the objects detected corresponding to single bright pixels are eliminated.

(iii) From the results obtained with steps (i) and (ii), the coordinates (in pixels) of each image are registered against the first image. Note that the images taken of the same field are usually not exactly centered at the same place both because of the accuracy of the telescope pointing system and because it is advisable, in order to make the flat-field, to slightly move the telescope between each image.

(iv) The seeing is estimated for each image and an image having the best seeing is selected. Within this image some objects are classified as "candidate TNOs" because of their small size and brightness. Indeed their size does not exceed the radius of a point-like object (criterion (b) mentioned above) and their central brightness (averaged over the 9 central pixels) does not exceed 100 times the threshold of detection. These two criteria limit to about 4 or 5 magnitudes the magnitude range corresponding to the search for new TNOs (i.e. typically 20 to 24-25).

(v) The other images are then searched for the equivalent objects as shown in Fig. 1. The key parameters, available as free parameters for the user, are: (i) the angles [FORMULA] and [FORMULA], relative to a vector direction (this vector represents the ecliptic plane oriented in the retrograde direction), [FORMULA] and [FORMULA] can be, typically, about -10o to +10o, covering all the possible apparent motions of the TNOs, and (ii) the interval of velocity motion (expressed in arcsec/hr) with 2 to 4 considered typically as acceptable. Of course, the scale of the image (expressed in arcsec/pixel) is a parameter needed by the program. From an object detected in the image having the best seeing another object is searched first in the following image and, eventually, in the other images (see Fig. 1). This procedure corresponds to the criteria (a) and (d) mentioned above.

[FIGURE] Fig. 1. Schematic view of how the apparent motion of a "candidate TNO" is tested by the program. For an object detected in a first image (position 1) a dashed area appearing around point 2 corresponds to the area where one could expect the object 1 to be located if it has moved like a TNO. Angles [FORMULA] and [FORMULA] are defined by the user and can be typically +10o and -10o. dmin and dmax, expressed in pixels, are computed by using the acceptable velocity range and the time elapsed between the images 1 and 2. If an object is found in the area 2 its motion is extrapolated and another object is searched in the area 3. This area is a simple square of 10 pixels size centered in the inferred position.

(vi) If an object satisfying the above-mentioned conditions is detected in at least three images another test is performed concerning its brightness: the average difference between the central brightness appearing in the different images and the mean of these values should not exceed 40% of this last value (criterion (c) mentioned above).

(vii) Finally if all these tests have been successful two possibilities can be examined. The first case consists in a good detection in all the images available. In this case the detection is considered secure and the "alarm" is triggered. The second case consists of missing detections in one or several images. In this case the seeing is examined and, if it is degraded by more than 30% (compared to the best one) in the images where the detection is missing, an "alarm" can also be triggered.

Finally, the program announces the possible detections, giving for each object its position in the different images. It is possible to visually check the detection by displaying a unique and composite frame consisting of the area around the object for all the images. The program can be used with images that have only been flat-fielded and bias-subtracted. Nevertheless, completely processed and calibrated images are, of course, preferable.

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© European Southern Observatory (ESO) 1999

Online publication: August 13, 199